----- What: ----- This is the readme file for the causal structure discovery weighted maxSAT data sets. These data sets are part of publication: J. Berg, A. Hyttinen, M. Järvisalo: "Applications of MaxSAT in Data Analysis" ---------- References ---------- The data sets are the product of the following original machine learning research papers: A. Hyttinen, F. Eberhardt, and M. Järvisalo: "Constraint-based Causal Discovery: Conflict Resolution with Answer Set Programming", Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, 2014. A. Hyttinen, P. O. Hoyer, F. Eberhardt, and M. Järvisalo "Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure", Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, 2013. Also presented at Pragmatics of SAT workshop 2013 and Approaches to Causal Structure Learning Workshop 2013. ----------------------- Causal Model Specifics ----------------------- Causal discovery instances were generated from linear Gaussian causal models (cycles allowed, coefs plus/minus 0.2-0.8), with 5-7 observed variables each. The average degree of the models was 2, the independence test employed was based Bayesian model selection approximation with BIC. Three different weighting schemes were considered: 1) log-weights (`log'), 2) all the constraints all have unit weights (`constant'), and instances 3) where separability constraints have unit weights while reachability constraints have infinite weights (`harddeps'). For the log-weights both the real and the rounded integer version of the instances are included. ----------------------- SELECTION OF INSTANCES ----------------------- First the instances were generated: -number of variables from 5 - 7 -instances 1 - 10 -samplesizes 500, 1000, 10000 -objective functions log, harddeps, constant -two encodings: uai13 and uai14 (uai13 only up to 6 variables) Instances such that - solving time using MaxHS solver was between 60s - 7200s - for instances with real and integer weights, both solving times had to be in the range (The weighting schemes, including whether integer or real weights were used have considerably different running times.) - objective function was greater than zero were selected to the data set. ----------- FILE NAMES ----------- Files are named following convention: causal_n_i_N___.wcnf where = '5','6', OR '7', number of observed variables in the causal graph = '1',...,'10', instance (seed) of the problem = '500','1000', OR '10000', the number of samples = 'uai13' OR 'uai14', the encoding used. 'uai13' is the encoding with recursion over path length (Hyttinen et al. 2013) and 'uai14' is the encoding over conditioning and marginalization operations (Hyttinen et al. 2014) = 'log','constant', OR 'harddeps', the type of weight, see Hyttinen et al. 2014 = 'dec' OR 'int', whether the weights of the soft clauses are decimal or integer. Decimal weights are used only with the 'log'-objective function. ------- CONTACT ------- In case of questions please check the original papers first, then you can contact: Antti Hyttinen email: antti.hyttinen@helsinki.fi --------- DATASETS: --------- The first number after the file name is the running time in seconds for MaxHS. The second number shows the optimal objective function value. The integer weights package includes all instances without (dec). The real weight package includes the decimal versions of the instances where it is available. These are labeled by (dec) below. 1 : causal_n5_i2_N500_uai13_harddeps_int.wcnf 85.68 5 2 : causal_n5_i4_N500_uai13_harddeps_int.wcnf 72.23 4 3 : causal_n5_i5_N500_uai13_log_int.wcnf 90.46 46030289 3 (dec): causal_n5_i5_N500_uai13_log_dec.wcnf 69.19 4.603029 4 : causal_n5_i5_N500_uai13_constant_int.wcnf 231.51 5 5 : causal_n5_i7_N500_uai13_harddeps_int.wcnf 90.57 17 6 : causal_n5_i7_N500_uai13_constant_int.wcnf 134.83 11 7 : causal_n5_i8_N500_uai13_harddeps_int.wcnf 201.56 18 8 : causal_n5_i9_N500_uai13_harddeps_int.wcnf 130.49 17 9 : causal_n5_i9_N500_uai13_constant_int.wcnf 1124.17 12 10 : causal_n5_i10_N500_uai13_log_int.wcnf 110.54 75755143 10 (dec): causal_n5_i10_N500_uai13_log_dec.wcnf 72.72 7.575514 11 : causal_n5_i10_N500_uai13_constant_int.wcnf 77.79 8 12 : causal_n5_i5_N1000_uai13_log_int.wcnf 71.89 46030289 12 (dec): causal_n5_i5_N1000_uai13_log_dec.wcnf 66.71 4.603029 13 : causal_n5_i5_N1000_uai13_constant_int.wcnf 68 5 14 : causal_n5_i7_N1000_uai13_harddeps_int.wcnf 129.99 17 15 : causal_n5_i7_N1000_uai13_constant_int.wcnf 150.87 11 16 : causal_n5_i8_N1000_uai13_harddeps_int.wcnf 147.45 18 17 : causal_n5_i9_N1000_uai13_log_int.wcnf 294.21 127884075 17 (dec): causal_n5_i9_N1000_uai13_log_dec.wcnf 174.37 12.78841 18 : causal_n5_i9_N1000_uai13_harddeps_int.wcnf 687.65 17 19 : causal_n5_i9_N1000_uai13_constant_int.wcnf 172.68 12 20 : causal_n5_i10_N1000_uai13_log_int.wcnf 179.91 75755143 20 (dec): causal_n5_i10_N1000_uai13_log_dec.wcnf 104.35 7.575514 21 : causal_n5_i5_N10000_uai13_log_int.wcnf 68.23 46030289 21 (dec): causal_n5_i5_N10000_uai13_log_dec.wcnf 69.59 4.603029 22 : causal_n5_i5_N10000_uai13_constant_int.wcnf 72.47 5 23 : causal_n5_i7_N10000_uai13_harddeps_int.wcnf 91.45 17 24 : causal_n5_i7_N10000_uai13_constant_int.wcnf 217.11 11 25 : causal_n5_i8_N10000_uai13_harddeps_int.wcnf 114.7 18 26 : causal_n5_i9_N10000_uai13_log_int.wcnf 252.87 127884075 26 (dec): causal_n5_i9_N10000_uai13_log_dec.wcnf 365.85 12.78841 27 : causal_n5_i9_N10000_uai13_harddeps_int.wcnf 86.59 17 28 : causal_n5_i9_N10000_uai13_constant_int.wcnf 175.07 12 29 : causal_n5_i10_N10000_uai13_constant_int.wcnf 63.58 8 30 : causal_n6_i1_N500_uai13_harddeps_int.wcnf 4702.93 19 31 : causal_n6_i2_N500_uai13_log_int.wcnf 3337.37 877436991 31 (dec): causal_n6_i2_N500_uai13_log_dec.wcnf 3991.77 8.77437 32 : causal_n6_i2_N500_uai14_harddeps_int.wcnf 250.89 48 33 : causal_n6_i3_N500_uai14_harddeps_int.wcnf 132.09 56 34 : causal_n6_i4_N500_uai14_constant_int.wcnf 70.67 17 35 : causal_n6_i5_N500_uai13_log_int.wcnf 773.81 355929820 35 (dec): causal_n6_i5_N500_uai13_log_dec.wcnf 3581.55 3.559298 36 : causal_n6_i5_N500_uai13_harddeps_int.wcnf 1198.27 4 37 : causal_n6_i5_N500_uai13_constant_int.wcnf 603.76 4 38 : causal_n6_i9_N500_uai14_constant_int.wcnf 222.38 28 39 : causal_n6_i10_N500_uai13_log_int.wcnf 5685.1 183312821 39 (dec): causal_n6_i10_N500_uai13_log_dec.wcnf 5084.09 18.33128 40 : causal_n6_i10_N500_uai14_log_int.wcnf 79.74 183312821 40 (dec): causal_n6_i10_N500_uai14_log_dec.wcnf 79.34 18.33128 41 : causal_n6_i10_N500_uai14_harddeps_int.wcnf 134.25 33 42 : causal_n6_i10_N500_uai14_constant_int.wcnf 229.95 28 43 : causal_n6_i2_N1000_uai13_log_int.wcnf 3883.69 877436991 43 (dec): causal_n6_i2_N1000_uai13_log_dec.wcnf 4663.3 8.77437 44 : causal_n6_i2_N1000_uai13_constant_int.wcnf 6852.21 15 45 : causal_n6_i2_N1000_uai14_harddeps_int.wcnf 210.26 48 46 : causal_n6_i3_N1000_uai14_harddeps_int.wcnf 352.36 56 47 : causal_n6_i4_N1000_uai14_constant_int.wcnf 63.64 17 48 : causal_n6_i5_N1000_uai13_log_int.wcnf 839.8 355929820 48 (dec): causal_n6_i5_N1000_uai13_log_dec.wcnf 688.15 3.559298 49 : causal_n6_i5_N1000_uai13_harddeps_int.wcnf 387.32 4 50 : causal_n6_i5_N1000_uai13_constant_int.wcnf 2489.36 4 51 : causal_n6_i6_N1000_uai14_log_int.wcnf 114.13 126257527700 51 (dec): causal_n6_i6_N1000_uai14_log_dec.wcnf 139.17 12.62575 52 : causal_n6_i6_N1000_uai14_constant_int.wcnf 205.91 19 53 : causal_n6_i7_N1000_uai14_log_int.wcnf 64.14 1633212419 53 (dec): causal_n6_i7_N1000_uai14_log_dec.wcnf 62.53 16.33212 54 : causal_n6_i7_N1000_uai14_harddeps_int.wcnf 63.96 49 55 : causal_n6_i8_N1000_uai14_log_int.wcnf 84.33 19596713347 55 (dec): causal_n6_i8_N1000_uai14_log_dec.wcnf 73.33 19.59671 56 : causal_n6_i8_N1000_uai14_constant_int.wcnf 73.05 26 57 : causal_n6_i9_N1000_uai14_constant_int.wcnf 166 28 58 : causal_n6_i10_N1000_uai14_constant_int.wcnf 83.41 28 59 : causal_n6_i1_N10000_uai14_log_int.wcnf 82.18 1510725680 59 (dec): causal_n6_i1_N10000_uai14_log_dec.wcnf 89.28 15.10726 60 : causal_n6_i1_N10000_uai14_constant_int.wcnf 279.15 19 61 : causal_n6_i2_N10000_uai14_harddeps_int.wcnf 140.47 48 62 : causal_n6_i3_N10000_uai13_log_int.wcnf 4635.73 10860281582 62 (dec): causal_n6_i3_N10000_uai13_log_dec.wcnf 3448.05 10.86028 63 : causal_n6_i3_N10000_uai14_harddeps_int.wcnf 132.68 56 64 : causal_n6_i3_N10000_uai14_constant_int.wcnf 63.95 22 65 : causal_n6_i5_N10000_uai13_log_int.wcnf 925.38 355929820 65 (dec): causal_n6_i5_N10000_uai13_log_dec.wcnf 901.59 3.559298 66 : causal_n6_i5_N10000_uai13_harddeps_int.wcnf 258.08 4 67 : causal_n6_i5_N10000_uai13_constant_int.wcnf 329.37 4 68 : causal_n6_i8_N10000_uai14_constant_int.wcnf 101.03 26 69 : causal_n6_i9_N10000_uai14_log_int.wcnf 116.65 1913093684 69 (dec): causal_n6_i9_N10000_uai14_log_dec.wcnf 111.75 19.13094 70 : causal_n6_i9_N10000_uai14_harddeps_int.wcnf 113.43 34 71 : causal_n6_i9_N10000_uai14_constant_int.wcnf 717.37 28 72 : causal_n7_i2_N500_uai14_harddeps_int.wcnf 5906.72 63 73 : causal_n7_i4_N500_uai14_log_int.wcnf 4119.74 37532020924 73 (dec): causal_n7_i4_N500_uai14_log_dec.wcnf 5341.45 37.53202 74 : causal_n7_i4_N500_uai14_harddeps_int.wcnf 2132.8 101 75 : causal_n7_i4_N500_uai14_constant_int.wcnf 5481.2 63 76 : causal_n7_i5_N500_uai14_log_int.wcnf 717.61 20711646820 76 (dec): causal_n7_i5_N500_uai14_log_dec.wcnf 5061.17 20.71165 77 : causal_n7_i5_N500_uai14_constant_int.wcnf 1797.03 48 78 : causal_n7_i6_N500_uai14_harddeps_int.wcnf 3330.67 116 79 : causal_n7_i8_N500_uai14_log_int.wcnf 66.97 11486104693 79 (dec): causal_n7_i8_N500_uai14_log_dec.wcnf 62.57 11.48611 80 : causal_n7_i8_N500_uai14_harddeps_int.wcnf 4768.39 94 81 : causal_n7_i8_N500_uai14_constant_int.wcnf 445.34 24 82 : causal_n7_i9_N500_uai14_log_int.wcnf 1153.35 43638470640 82 (dec): causal_n7_i9_N500_uai14_log_dec.wcnf 5056.74 43.63847 83 : causal_n7_i9_N500_uai14_harddeps_int.wcnf 1344 82 84 : causal_n7_i9_N500_uai14_constant_int.wcnf 2091.97 46 85 : causal_n7_i10_N500_uai14_log_int.wcnf 1731.66 3246397504 85 (dec): causal_n7_i10_N500_uai14_log_dec.wcnf 1355.17 32.46397 86 : causal_n7_i10_N500_uai14_constant_int.wcnf 1993.56 42 87 : causal_n7_i4_N1000_uai14_log_int.wcnf 6940.5 37532020924 87 (dec): causal_n7_i4_N1000_uai14_log_dec.wcnf 6958.81 37.53202 88 : causal_n7_i4_N1000_uai14_harddeps_int.wcnf 2433.89 101 89 : causal_n7_i4_N1000_uai14_constant_int.wcnf 6870.64 63 90 : causal_n7_i5_N1000_uai14_log_int.wcnf 724.92 20711646820 90 (dec): causal_n7_i5_N1000_uai14_log_dec.wcnf 3256.99 20.71165 91 : causal_n7_i5_N1000_uai14_constant_int.wcnf 2024.09 48 92 : causal_n7_i6_N1000_uai14_harddeps_int.wcnf 3080.56 116 93 : causal_n7_i7_N1000_uai14_harddeps_int.wcnf 2424.15 95 94 : causal_n7_i8_N1000_uai14_log_int.wcnf 111.25 11486104693 94 (dec): causal_n7_i8_N1000_uai14_log_dec.wcnf 105.17 11.48611 95 : causal_n7_i8_N1000_uai14_harddeps_int.wcnf 4510.2 94 96 : causal_n7_i8_N1000_uai14_constant_int.wcnf 163.61 24 97 : causal_n7_i9_N1000_uai14_log_int.wcnf 1180.14 43638470640 97 (dec): causal_n7_i9_N1000_uai14_log_dec.wcnf 1154.8 43.63847 98 : causal_n7_i9_N1000_uai14_harddeps_int.wcnf 1539.13 82 99 : causal_n7_i9_N1000_uai14_constant_int.wcnf 1677.26 46 100 : causal_n7_i10_N1000_uai14_log_int.wcnf 1466.53 3246397504 100 (dec): causal_n7_i10_N1000_uai14_log_dec.wcnf 976.56 32.46397 101 : causal_n7_i10_N1000_uai14_constant_int.wcnf 840.48 42 102 : causal_n7_i2_N10000_uai14_harddeps_int.wcnf 1599.56 63 103 : causal_n7_i4_N10000_uai14_log_int.wcnf 5369.96 37532020924 103 (dec): causal_n7_i4_N10000_uai14_log_dec.wcnf 5830.19 37.53202 104 : causal_n7_i4_N10000_uai14_harddeps_int.wcnf 1865.64 101 105 : causal_n7_i5_N10000_uai14_log_int.wcnf 893.21 20711646820 105 (dec): causal_n7_i5_N10000_uai14_log_dec.wcnf 719.71 20.71165 106 : causal_n7_i5_N10000_uai14_constant_int.wcnf 2076.48 48 107 : causal_n7_i6_N10000_uai14_harddeps_int.wcnf 2399.77 116 108 : causal_n7_i7_N10000_uai14_harddeps_int.wcnf 2434.16 95 109 : causal_n7_i8_N10000_uai14_log_int.wcnf 89.13 11486104693 109 (dec): causal_n7_i8_N10000_uai14_log_dec.wcnf 97.61 11.48611 110 : causal_n7_i8_N10000_uai14_harddeps_int.wcnf 3986.73 94 111 : causal_n7_i8_N10000_uai14_constant_int.wcnf 128 24 112 : causal_n7_i9_N10000_uai14_log_int.wcnf 957.7 43638470640 112 (dec): causal_n7_i9_N10000_uai14_log_dec.wcnf 1032.49 43.63847 113 : causal_n7_i9_N10000_uai14_harddeps_int.wcnf 1879.44 82 114 : causal_n7_i9_N10000_uai14_constant_int.wcnf 1213.72 46 115 : causal_n7_i10_N10000_uai14_log_int.wcnf 2047.54 3246397504 115 (dec): causal_n7_i10_N10000_uai14_log_dec.wcnf 2516.95 32.46397 116 : causal_n7_i10_N10000_uai14_constant_int.wcnf 1980.04 42